Risk Averse, Risk Neutral, and Risk Acceptant Preferences

Someone with risk neutral preferences simply wants to maximize their expected value. For example, consider a lottery that gives $1 million 50% of the time and $0 50% of the time. A risk neutral person would be indifferent between that lottery and receiving $500,000 with certainty.

Someone with risk averse preferences is willing to take an amount of money smaller than the expected value of a lottery. In the 50/50 lottery between $1 million and $0, a risk averse person would be indifferent at an amount strictly less than $500,000.

Risk aversion means that an individual values each dollar less than the previous. These preferences explain why people buy insurance.

Someone with risk accceptant preferences requires an amount of money greater than the expected value of a lottery to be bought out. In the 50/50 lottery between $1 million and $0, a risk averse person would be indifferent at an amount strictly greater than $500,000.

Risk acceptance means that an individual values each dollar more than the previous. Someone with such preferences would exhibit behaviors similar to a compulsive gambler.

We can use exponents to conveniently represent these preferences. Consider the utility function xa, where x is the amount of money an individual receives. a = 1 represents risk neutral preferences; a > 1 represents risk acceptant preferences; a < 1 represents risk averse preferences.

Nothing in expected utility theory prevents us from modeling risk preferences. However, those preferences should be directly built into the payoffs you enter into a game matrix.